SECTION A

  1. What can you say about the factors of the denominator of the rational number 10.25
  2.  and  are the zeros of the polynomial 2x2+ 3x + 4 find the value of 1/+ 1/
  3. For what value of k the following equation will be a quadratic equation (2k -1)x2+ kx + 3 =0.
  4. The largest right circular cone is carved out of a cube of edge p units. Find the volume.

5Cards are numbered from 7 to 51, one card is drawn at random find the probability of getting smallest composite number

6.Check whether 301 is a term of A.P. 5, 11, 17, 23…

7A ladder 24cm long reaches a window of a house 12 m above the ground. If the distance of the foot of the ladder from the house.

8If A+B = 90 and sec A = 4/3 find cosec B

9The length of tangent drawn to a circle from a point at a distance of 5cm from the center is 4cm. Find the radius of the circle. O

10What are the angles of depression from the observing 30

point O of the objects at A and B. 45

A C

SECTION B

B D

11What must be added to the polynomial 5x4+ 6x3– 13x2– 44x + 7 so that the resulting polynomial is divisible by x2+ 4x + 3.

12.For what values of a and b the following system of equations have infinite many solutions: 3x – (a + 1) y = 2b – 1 and 5x + ( 1- 2a) y = 3b

C A

13.In figure, PA and PB are the tangents to the circle drawn

from the external point P, CD is another tangent touching P Q

the circle at Q. If PB = 10 cm, find the perimeter of PCD. D B

.

14.The length of a line segment is 10. If one end is at (2, -3) and the abscissa of the second end is 10. Show that its ordinate is either 3 or -9.

15.Evaluate : 4(sin430 + cos460) – 3(cos245 - sin290) + (sin260 + sin245)

SECTION C

16.Radius of a circular track is 63m. Two cyclists Sonu and Mohit start together from the same point and in same direction with speeds 33m/min and 44m/min respectively. After how many minutes thy meet again at the starting point?

17.A two digit number can be obtained either multiplying the sum of the digits by 8 or multiplying the difference of the digits by 14 and adding 2. Find the number.

18.Solve: x – a + x – b = a + b

x – b x – a b a

19.Find the sum of integers between 100 and 700 which on dividing by 11 leave a remainder 7

20.P and Q are the points on sides CA and CB respectively of ABC, right angled at C. Prove that AQ2 + BP2= AB2+ PQ2

21.The line segment joining the points (3, -4) and (1, 2) is trisected at the points (a, -2) and Q(5/3, b), find the values of a and b.

22.Prove : √ sec2 A + cosec2A = tanA + cotA

.OR

sec210 - cot280 sin15cos75 + cos15sin75

cos sin(90 - ) + sin cos(90 -)

23.Let ABC is a right triangle in which AB = 3cm, BC = 4cmand B = 90. BD is perpendicular from B on AC. The circle through B, C, and D is drawn. Construct the pair of tangents from the point A to the circle.

24.The cost of fencing a circular field at the rate of Rs. 16 per meter is Rs. 3014.4.The field is to be ploughed at the rate of Rs. 0.40 per m2. Find the cost of ploughing the field. ( ∏ = 3.14)

25.Water is flowing at the rate of 5km per hour through a pipe of diameter 14cm into a rectangular tank which is 25m long and 22m wide. Determine the time in which the water level rises by 21cm.

SECTION D

26.A tree stands vertically on the bank of a river. From a point on the other bank directly opposite the tree, the angle of elevation of the top of the tree is 60. From a point 20m behind this point on the same bank, the angle of elevation of the top of the tree is30. Find the height of the tree and the width of the river.

27.A bucket of height 16cm and made up of metal sheet is in the form of frustum of a cone with radii of its lower and upper ends are 3cm and 15cm respectively: Calculate (i) Volume of water that can be filled (ii) the slant height of the bucket (iii) area of metal sheet required

28.If the median of the following data is 27, find the values of x and y

C. I.0 – 10 10 – 2020 – 30 30 – 4040 – 5050 – 60 f 5 x 20 14 y 8 = 68

29. State and prove converse of the following: In a triangle if the square of one side is equal to the sum of the square of the other two sides then the angle opposite to the first side if right angle. Using this theorem: prove that

In an equilateral triangle ABC, AD is an altitude drawn from A on side BC. Prove that 3AB2= 4AD2

30.A man sold a table & a chair together for Rs. 850 at a loss of 10% on the table and a gain of 10% on the chair. By selling them for Rs. 950, he would have made a gain of 10% on the table and 10% loss on the chair. Find the cost price of each.